Theorems · Definition · number theory
NumberField.mixedEmbedding.minkowskiBound
(K : Type u_1) →
[inst : Field K] →
[inst_1 : NumberField K] → (FractionalIdeal (nonZeroDivisors (NumberField.RingOfIntegers K)) K)ˣ → ENNRealThe bound that appears in Minkowski Convex Body theorem, see
MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure. See
NumberField.mixedEmbedding.volume_fundamentalDomain_idealLatticeBasis_eq and
NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis for the computation of
volume (fundamentalDomain (idealLatticeBasis K)).
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 309 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realproof · cited by 25,697
- ENNRealstatement · cited by 9,879
- Fieldstatement and proof · cited by 7,404
- Unitsstatement and proof · cited by 2,804
- Module.finrankproof · cited by 1,770
- MeasureTheory.MeasureSpace.volumeproof · cited by 1,323
- nonZeroDivisorsstatement and proof · cited by 895
- NumberFieldstatement and proof · cited by 653
- FractionalIdealstatement and proof · cited by 423
- NumberField.RingOfIntegersstatement and proof · cited by 413
- NumberField.mixedEmbedding.mixedSpaceproof · cited by 239
Cited by22
Results whose statement or proof uses this declaration.
- NumberField.Units.dirichletUnitTheorem.seqstatement and proof · cited by 6
- NumberField.Units.dirichletUnitTheorem.seq_nextstatement and proof · cited by 3
- NumberField.hermiteTheorem.minkowskiBound_lt_boundOfDiscBddstatement · cited by 2
- NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_lestatement and proof · cited by 2
- NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_ltstatement and proof · cited by 2
- NumberField.mixedEmbedding.minkowskiBound_lt_topstatement · cited by 2
- NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discrproof · cited by 2
- NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplexproof · cited by 1
- NumberField.hermiteTheorem.finite_of_discr_bdd_of_isRealproof · cited by 1
- NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_ltstatement and proof · cited by 1
- NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt'statement and proof · cited by 1
- NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt'statement and proof · cited by 1